A wire made from copper with a cross-section of diameter 0.980 mm carries a curr

Question

A wire made from copper with a cross-section of diameter 0.980 mm carries a current of 14.0 A. Calculate the "areal current density"; in other words, how many electrons per square meter per second flow through this wire? (Enter your answer without units.)

The density of copper is 8.95 g/cm3, and its atomic mass is 63.8. Assuming each copper atom contributes one mobile electron to the metal, what is the number density of free charges in the wire, in electrons/m3? (Enter your answer without units.)

How many atoms of copper are in one gram? (Remember your chemistry...)

Use your results to calculate the drift speed (i.e., the average net speed) of the electrons in the wire. This can be answered through dimensional analysis: how can you combine your previous results to get the dimensions of speed?

Due to thermal motion, the electrons at room temperature are randomly traveling to and fro at 1.16×105 m/s, even without any current. What fraction is the current's drift speed, compared to the random thermal motion?

Explanation / Answer

a)

14.A means 14.0 C of charge per second passing a given point.

This corresponds to 14/1.60x10^-19 = 8.75x10^19 electrons per second
or equivalently an electron density of 8.75x10^19/(*(0.490x10^-3)^2) = 1.159x10^26 electron per m^2 per second

B) There are 8.95g/cm^3/63.8g/mol*6.022x10^23molecule... electron/molecule
= 0.844x10^23 electron/cm^3 = 0.844x10^29 electrons/m^3

C) Drifty Speed, vd = J/(n*q) = 14.0/(*(0.490x10^-3)^2)/(0.844x10^29*1.6*10^-19). = 1.366x10^-3m/s

D) Fraction is given by 1.366x10^-3/1.16x10^5 = 1.177x10^-8

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